Question

Let f be defined as shown on the graph. Which statement is true?

1: The inverse of f exists
2: The inverse of f does NOT exist

Answer 1

The inverse of f does NOT exist. The reason why is because the function fails the horizontal line test. Recall that the horizontal line test is a test where you try to see if you can pass a single horizontal line through more than one point on the function curve. If you can get the horizontal line to pass through more than one point, then it fails the test. It's very similar to the vertical line test.